boost::numeric::odeint::velocity_verlet< Coor, Velocity, Value, Acceleration, Time, TimeSq, Algebra, Operations, Resizer > Class Template Reference

The Velocity-Verlet algorithm. More...

#include <velocity_verlet.hpp>

Inheritance diagram for boost::numeric::odeint::velocity_verlet< Coor, Velocity, Value, Acceleration, Time, TimeSq, Algebra, Operations, Resizer >:

Collaboration diagram for boost::numeric::odeint::velocity_verlet< Coor, Velocity, Value, Acceleration, Time, TimeSq, Algebra, Operations, Resizer >:

Public Types
typedef algebra_stepper_base < Algebra, Operations >	algebra_stepper_base_type
typedef algebra_stepper_base_type::algebra_type	algebra_type
typedef algebra_stepper_base_type::operations_type	operations_type
typedef Coor	coor_type
typedef Velocity	velocity_type
typedef Acceleration	acceleration_type
typedef std::pair< coor_type, velocity_type >	state_type
typedef std::pair < velocity_type, acceleration_type >	deriv_type
typedef state_wrapper < acceleration_type >	wrapped_acceleration_type
typedef Value	value_type
typedef Time	time_type
typedef TimeSq	time_square_type
typedef Resizer	resizer_type
typedef stepper_tag	stepper_category
typedef unsigned short	order_type

Public Member Functions
order_type	order (void) const
	velocity_verlet (const algebra_type &algebra=algebra_type())
	Constructs the velocity_verlet class. More...
template<class System , class StateInOut >
void	do_step (System system, StateInOut &x, time_type t, time_type dt)
	This method performs one step. More...
template<class System , class StateInOut >
void	do_step (System system, const StateInOut &x, time_type t, time_type dt)
	This method performs one step. More...
template<class System , class CoorIn , class VelocityIn , class AccelerationIn , class CoorOut , class VelocityOut , class AccelerationOut >
void	do_step (System system, CoorIn const &qin, VelocityIn const &pin, AccelerationIn const &ain, CoorOut &qout, VelocityOut &pout, AccelerationOut &aout, time_type t, time_type dt)
	This method performs one step. More...
template<class StateIn >
void	adjust_size (const StateIn &x)
	Adjust the size of all temporaries in the stepper manually. More...
void	reset (void)
	Resets the internal state of this stepper. More...
template<class AccelerationIn >
void	initialize (const AccelerationIn &ain)
	Initializes the internal state of the stepper. More...
template<class System , class CoorIn , class VelocityIn >
void	initialize (System system, const CoorIn &qin, const VelocityIn &pin, time_type t)
	Initializes the internal state of the stepper. More...
bool	is_initialized (void) const
algebra_type &	algebra ()
const algebra_type &	algebra () const

Static Public Attributes
static const order_type	order_value = 1

Protected Attributes
algebra_type	m_algebra

Detailed Description

template<class Coor, class Velocity = Coor, class Value = double, class Acceleration = Coor, class Time = Value, class TimeSq = Time, class Algebra = typename algebra_dispatcher< Coor >::algebra_type, class Operations = typename operations_dispatcher< Coor >::operations_type, class Resizer = initially_resizer>
class boost::numeric::odeint::velocity_verlet< Coor, Velocity, Value, Acceleration, Time, TimeSq, Algebra, Operations, Resizer >

The Velocity-Verlet algorithm.

The Velocity-Verlet algorithm is a method for simulation of molecular dynamics systems. It solves the ODE a=f(r,v',t) where r are the coordinates, v are the velocities and a are the accelerations, hence v = dr/dt, a=dv/dt.

Template Parameters

Coor	The type representing the coordinates.
Velocity	The type representing the velocities.
Value	The type value type.
Acceleration	The type representing the acceleration.
Time	The time representing the independent variable - the time.
TimeSq	The time representing the square of the time.
Algebra	The algebra.
Operations	The operations type.
Resizer	The resizer policy type.

Member Typedef Documentation

template<class Coor , class Velocity = Coor, class Value = double, class Acceleration = Coor, class Time = Value, class TimeSq = Time, class Algebra = typename algebra_dispatcher< Coor >::algebra_type, class Operations = typename operations_dispatcher< Coor >::operations_type, class Resizer = initially_resizer>

typedef Acceleration boost::numeric::odeint::velocity_verlet< Coor, Velocity, Value, Acceleration, Time, TimeSq, Algebra, Operations, Resizer >::acceleration_type

template<class Coor , class Velocity = Coor, class Value = double, class Acceleration = Coor, class Time = Value, class TimeSq = Time, class Algebra = typename algebra_dispatcher< Coor >::algebra_type, class Operations = typename operations_dispatcher< Coor >::operations_type, class Resizer = initially_resizer>

typedef algebra_stepper_base< Algebra , Operations > boost::numeric::odeint::velocity_verlet< Coor, Velocity, Value, Acceleration, Time, TimeSq, Algebra, Operations, Resizer >::algebra_stepper_base_type

template<class Coor , class Velocity = Coor, class Value = double, class Acceleration = Coor, class Time = Value, class TimeSq = Time, class Algebra = typename algebra_dispatcher< Coor >::algebra_type, class Operations = typename operations_dispatcher< Coor >::operations_type, class Resizer = initially_resizer>

typedef algebra_stepper_base_type::algebra_type boost::numeric::odeint::velocity_verlet< Coor, Velocity, Value, Acceleration, Time, TimeSq, Algebra, Operations, Resizer >::algebra_type

template<class Coor , class Velocity = Coor, class Value = double, class Acceleration = Coor, class Time = Value, class TimeSq = Time, class Algebra = typename algebra_dispatcher< Coor >::algebra_type, class Operations = typename operations_dispatcher< Coor >::operations_type, class Resizer = initially_resizer>

typedef Coor boost::numeric::odeint::velocity_verlet< Coor, Velocity, Value, Acceleration, Time, TimeSq, Algebra, Operations, Resizer >::coor_type

template<class Coor , class Velocity = Coor, class Value = double, class Acceleration = Coor, class Time = Value, class TimeSq = Time, class Algebra = typename algebra_dispatcher< Coor >::algebra_type, class Operations = typename operations_dispatcher< Coor >::operations_type, class Resizer = initially_resizer>

typedef std::pair< velocity_type , acceleration_type > boost::numeric::odeint::velocity_verlet< Coor, Velocity, Value, Acceleration, Time, TimeSq, Algebra, Operations, Resizer >::deriv_type

template<class Coor , class Velocity = Coor, class Value = double, class Acceleration = Coor, class Time = Value, class TimeSq = Time, class Algebra = typename algebra_dispatcher< Coor >::algebra_type, class Operations = typename operations_dispatcher< Coor >::operations_type, class Resizer = initially_resizer>

typedef algebra_stepper_base_type::operations_type boost::numeric::odeint::velocity_verlet< Coor, Velocity, Value, Acceleration, Time, TimeSq, Algebra, Operations, Resizer >::operations_type

template<class Coor , class Velocity = Coor, class Value = double, class Acceleration = Coor, class Time = Value, class TimeSq = Time, class Algebra = typename algebra_dispatcher< Coor >::algebra_type, class Operations = typename operations_dispatcher< Coor >::operations_type, class Resizer = initially_resizer>

typedef unsigned short boost::numeric::odeint::velocity_verlet< Coor, Velocity, Value, Acceleration, Time, TimeSq, Algebra, Operations, Resizer >::order_type

template<class Coor , class Velocity = Coor, class Value = double, class Acceleration = Coor, class Time = Value, class TimeSq = Time, class Algebra = typename algebra_dispatcher< Coor >::algebra_type, class Operations = typename operations_dispatcher< Coor >::operations_type, class Resizer = initially_resizer>

typedef Resizer boost::numeric::odeint::velocity_verlet< Coor, Velocity, Value, Acceleration, Time, TimeSq, Algebra, Operations, Resizer >::resizer_type

template<class Coor , class Velocity = Coor, class Value = double, class Acceleration = Coor, class Time = Value, class TimeSq = Time, class Algebra = typename algebra_dispatcher< Coor >::algebra_type, class Operations = typename operations_dispatcher< Coor >::operations_type, class Resizer = initially_resizer>

typedef std::pair< coor_type , velocity_type > boost::numeric::odeint::velocity_verlet< Coor, Velocity, Value, Acceleration, Time, TimeSq, Algebra, Operations, Resizer >::state_type

template<class Coor , class Velocity = Coor, class Value = double, class Acceleration = Coor, class Time = Value, class TimeSq = Time, class Algebra = typename algebra_dispatcher< Coor >::algebra_type, class Operations = typename operations_dispatcher< Coor >::operations_type, class Resizer = initially_resizer>

typedef stepper_tag boost::numeric::odeint::velocity_verlet< Coor, Velocity, Value, Acceleration, Time, TimeSq, Algebra, Operations, Resizer >::stepper_category

template<class Coor , class Velocity = Coor, class Value = double, class Acceleration = Coor, class Time = Value, class TimeSq = Time, class Algebra = typename algebra_dispatcher< Coor >::algebra_type, class Operations = typename operations_dispatcher< Coor >::operations_type, class Resizer = initially_resizer>

typedef TimeSq boost::numeric::odeint::velocity_verlet< Coor, Velocity, Value, Acceleration, Time, TimeSq, Algebra, Operations, Resizer >::time_square_type

template<class Coor , class Velocity = Coor, class Value = double, class Acceleration = Coor, class Time = Value, class TimeSq = Time, class Algebra = typename algebra_dispatcher< Coor >::algebra_type, class Operations = typename operations_dispatcher< Coor >::operations_type, class Resizer = initially_resizer>

typedef Time boost::numeric::odeint::velocity_verlet< Coor, Velocity, Value, Acceleration, Time, TimeSq, Algebra, Operations, Resizer >::time_type

template<class Coor , class Velocity = Coor, class Value = double, class Acceleration = Coor, class Time = Value, class TimeSq = Time, class Algebra = typename algebra_dispatcher< Coor >::algebra_type, class Operations = typename operations_dispatcher< Coor >::operations_type, class Resizer = initially_resizer>

typedef Value boost::numeric::odeint::velocity_verlet< Coor, Velocity, Value, Acceleration, Time, TimeSq, Algebra, Operations, Resizer >::value_type

template<class Coor , class Velocity = Coor, class Value = double, class Acceleration = Coor, class Time = Value, class TimeSq = Time, class Algebra = typename algebra_dispatcher< Coor >::algebra_type, class Operations = typename operations_dispatcher< Coor >::operations_type, class Resizer = initially_resizer>

typedef Velocity boost::numeric::odeint::velocity_verlet< Coor, Velocity, Value, Acceleration, Time, TimeSq, Algebra, Operations, Resizer >::velocity_type

template<class Coor , class Velocity = Coor, class Value = double, class Acceleration = Coor, class Time = Value, class TimeSq = Time, class Algebra = typename algebra_dispatcher< Coor >::algebra_type, class Operations = typename operations_dispatcher< Coor >::operations_type, class Resizer = initially_resizer>

typedef state_wrapper< acceleration_type > boost::numeric::odeint::velocity_verlet< Coor, Velocity, Value, Acceleration, Time, TimeSq, Algebra, Operations, Resizer >::wrapped_acceleration_type

Constructor & Destructor Documentation

template<class Coor , class Velocity = Coor, class Value = double, class Acceleration = Coor, class Time = Value, class TimeSq = Time, class Algebra = typename algebra_dispatcher< Coor >::algebra_type, class Operations = typename operations_dispatcher< Coor >::operations_type, class Resizer = initially_resizer>

boost::numeric::odeint::velocity_verlet< Coor, Velocity, Value, Acceleration, Time, TimeSq, Algebra, Operations, Resizer >::velocity_verlet ( const algebra_type &  algebra = algebra_type() )

inline

Constructs the velocity_verlet class.

This constructor can be used as a default constructor if the algebra has a default constructor.

Parameters

algebra

A copy of algebra is made and stored.

Member Function Documentation

template<class Coor , class Velocity = Coor, class Value = double, class Acceleration = Coor, class Time = Value, class TimeSq = Time, class Algebra = typename algebra_dispatcher< Coor >::algebra_type, class Operations = typename operations_dispatcher< Coor >::operations_type, class Resizer = initially_resizer>

template<class StateIn >

void boost::numeric::odeint::velocity_verlet< Coor, Velocity, Value, Acceleration, Time, TimeSq, Algebra, Operations, Resizer >::adjust_size ( const StateIn &  x )

inline

Adjust the size of all temporaries in the stepper manually.

Parameters

x	A state from which the size of the temporaries to be resized is deduced.

template<class Algebra, class Operations>

algebra_type & boost::numeric::odeint::algebra_stepper_base< Algebra, Operations >::algebra ( )

inlineinherited

Returns

A reference to the algebra which is held by this class.

template<class Algebra, class Operations>

const algebra_type & boost::numeric::odeint::algebra_stepper_base< Algebra, Operations >::algebra ( ) const

inlineinherited

Returns

A const reference to the algebra which is held by this class.

template<class Coor , class Velocity = Coor, class Value = double, class Acceleration = Coor, class Time = Value, class TimeSq = Time, class Algebra = typename algebra_dispatcher< Coor >::algebra_type, class Operations = typename operations_dispatcher< Coor >::operations_type, class Resizer = initially_resizer>

template<class System , class StateInOut >

boost::numeric::odeint::velocity_verlet< Coor, Velocity, Value, Acceleration, Time, TimeSq, Algebra, Operations, Resizer >::do_step ( System  system, StateInOut &  x, time_type  t, time_type  dt  )

inline

This method performs one step.

It transforms the result in-place.

It can be used like

pair< coordinates , velocities > state;
stepper.do_step( sys , x , t , dt );

Parameters

system	The system function to solve, hence the r.h.s. of the ordinary differential equation. It must fulfill the Second Order System concept.
x	The state of the ODE which should be solved. The state is pair of Coor and Velocity.
t	The value of the time, at which the step should be performed.
dt	The step size.

template<class Coor , class Velocity = Coor, class Value = double, class Acceleration = Coor, class Time = Value, class TimeSq = Time, class Algebra = typename algebra_dispatcher< Coor >::algebra_type, class Operations = typename operations_dispatcher< Coor >::operations_type, class Resizer = initially_resizer>

template<class System , class StateInOut >

boost::numeric::odeint::velocity_verlet< Coor, Velocity, Value, Acceleration, Time, TimeSq, Algebra, Operations, Resizer >::do_step ( System  system, const StateInOut &  x, time_type  t, time_type  dt  )

inline

This method performs one step.

It transforms the result in-place.

It can be used like

pair< coordinates , velocities > state;
stepper.do_step( sys , x , t , dt );

Parameters

system	The system function to solve, hence the r.h.s. of the ordinary differential equation. It must fulfill the Second Order System concept.
x	The state of the ODE which should be solved. The state is pair of Coor and Velocity.
t	The value of the time, at which the step should be performed.
dt	The step size.

template<class Coor , class Velocity = Coor, class Value = double, class Acceleration = Coor, class Time = Value, class TimeSq = Time, class Algebra = typename algebra_dispatcher< Coor >::algebra_type, class Operations = typename operations_dispatcher< Coor >::operations_type, class Resizer = initially_resizer>

template<class System , class CoorIn , class VelocityIn , class AccelerationIn , class CoorOut , class VelocityOut , class AccelerationOut >

boost::numeric::odeint::velocity_verlet< Coor, Velocity, Value, Acceleration, Time, TimeSq, Algebra, Operations, Resizer >::do_step ( System  system, CoorIn const &  qin, VelocityIn const &  pin, AccelerationIn const &  ain, CoorOut &  qout, VelocityOut &  pout, AccelerationOut &  aout, time_type  t, time_type  dt  )

inline

This method performs one step.

It transforms the result in-place. Additionally to the other methods the coordinates, velocities and accelerations are passed directly to do_step and they are transformed out-of-place.

It can be used like

coordinates qin , qout;
velocities pin , pout;
accelerations ain, aout;
stepper.do_step( sys , qin , pin , ain , qout , pout , aout , t , dt );

Parameters

system	The system function to solve, hence the r.h.s. of the ordinary differential equation. It must fulfill the Second Order System concept.
x	The state of the ODE which should be solved. The state is pair of Coor and Velocity.
t	The value of the time, at which the step should be performed.
dt	The step size.

References boost::numeric::odeint::algebra_stepper_base< Algebra, Operations >::m_algebra, template, and boost::detail::type.

template<class Coor , class Velocity = Coor, class Value = double, class Acceleration = Coor, class Time = Value, class TimeSq = Time, class Algebra = typename algebra_dispatcher< Coor >::algebra_type, class Operations = typename operations_dispatcher< Coor >::operations_type, class Resizer = initially_resizer>

template<class AccelerationIn >

boost::numeric::odeint::velocity_verlet< Coor, Velocity, Value, Acceleration, Time, TimeSq, Algebra, Operations, Resizer >::initialize ( const AccelerationIn &  qin )

inline

Initializes the internal state of the stepper.

Parameters

deriv

The acceleration of x. The next call of do_step expects that the acceleration of x passed to do_step has the value of qin.

References boost::numeric::odeint::detail::_1, boost::bind(), boost::numeric::odeint::copy(), boost::ref(), and template.

template<class Coor , class Velocity = Coor, class Value = double, class Acceleration = Coor, class Time = Value, class TimeSq = Time, class Algebra = typename algebra_dispatcher< Coor >::algebra_type, class Operations = typename operations_dispatcher< Coor >::operations_type, class Resizer = initially_resizer>

template<class System , class CoorIn , class VelocityIn >

boost::numeric::odeint::velocity_verlet< Coor, Velocity, Value, Acceleration, Time, TimeSq, Algebra, Operations, Resizer >::initialize ( System  system, const CoorIn &  qin, const VelocityIn &  pin, time_type  t  )

inline

Initializes the internal state of the stepper.

This method is equivalent to

Acceleration a;
system( qin , pin , a , t );
stepper.initialize( a );

Parameters

system	The system function for the next calls of do_step.
qin	The current coordinates of the ODE.
pin	The current velocities of the ODE.
t	The current time of the ODE.

References boost::numeric::odeint::detail::_1, boost::bind(), boost::ref(), and template.

template<class Coor , class Velocity = Coor, class Value = double, class Acceleration = Coor, class Time = Value, class TimeSq = Time, class Algebra = typename algebra_dispatcher< Coor >::algebra_type, class Operations = typename operations_dispatcher< Coor >::operations_type, class Resizer = initially_resizer>

boost::numeric::odeint::velocity_verlet< Coor, Velocity, Value, Acceleration, Time, TimeSq, Algebra, Operations, Resizer >::is_initialized ( void  ) const

inline

Returns

Returns if the stepper is initialized.

template<class Coor , class Velocity = Coor, class Value = double, class Acceleration = Coor, class Time = Value, class TimeSq = Time, class Algebra = typename algebra_dispatcher< Coor >::algebra_type, class Operations = typename operations_dispatcher< Coor >::operations_type, class Resizer = initially_resizer>

order_type boost::numeric::odeint::velocity_verlet< Coor, Velocity, Value, Acceleration, Time, TimeSq, Algebra, Operations, Resizer >::order ( void  ) const

inline

Returns

Returns the order of the stepper.

References boost::numeric::odeint::velocity_verlet< Coor, Velocity, Value, Acceleration, Time, TimeSq, Algebra, Operations, Resizer >::order_value.

template<class Coor , class Velocity = Coor, class Value = double, class Acceleration = Coor, class Time = Value, class TimeSq = Time, class Algebra = typename algebra_dispatcher< Coor >::algebra_type, class Operations = typename operations_dispatcher< Coor >::operations_type, class Resizer = initially_resizer>

boost::numeric::odeint::velocity_verlet< Coor, Velocity, Value, Acceleration, Time, TimeSq, Algebra, Operations, Resizer >::reset ( void  )

inline

Resets the internal state of this stepper.

After calling this method it is safe to use all do_step method without explicitly initializing the stepper.

Member Data Documentation

template<class Algebra, class Operations>

algebra_type boost::numeric::odeint::algebra_stepper_base< Algebra, Operations >::m_algebra

protectedinherited

Referenced by boost::numeric::odeint::algebra_stepper_base< algebra_type, operations_type >::algebra(), boost::numeric::odeint::euler< State, Value, Deriv, Time, Algebra, Operations, Resizer >::calc_state(), boost::numeric::odeint::runge_kutta_dopri5< State, Value, Deriv, Time, Algebra, Operations, Resizer >::calc_state(), boost::numeric::odeint::velocity_verlet< Coor, Velocity, Value, Acceleration, Time, TimeSq, Algebra, Operations, Resizer >::do_step(), boost::numeric::odeint::euler< State, Value, Deriv, Time, Algebra, Operations, Resizer >::do_step_impl(), boost::numeric::odeint::modified_midpoint< state_type, value_type, deriv_type, time_type, algebra_type, operations_type, resizer_type >::do_step_impl(), boost::numeric::odeint::runge_kutta4_classic< State, Value, Deriv, Time, Algebra, Operations, Resizer >::do_step_impl(), boost::numeric::odeint::runge_kutta_dopri5< State, Value, Deriv, Time, Algebra, Operations, Resizer >::do_step_impl(), boost::numeric::odeint::runge_kutta_cash_karp54_classic< State, Value, Deriv, Time, Algebra, Operations, Resizer >::do_step_impl(), boost::numeric::odeint::explicit_error_generic_rk< 6, 5, 5, 4, State, Value, Deriv, Time, Algebra, Operations, Resizer >::do_step_impl(), and boost::numeric::odeint::explicit_generic_rk< 4, 4, State, Value, Deriv, Time, Algebra, Operations, Resizer >::do_step_impl().

template<class Coor , class Velocity = Coor, class Value = double, class Acceleration = Coor, class Time = Value, class TimeSq = Time, class Algebra = typename algebra_dispatcher< Coor >::algebra_type, class Operations = typename operations_dispatcher< Coor >::operations_type, class Resizer = initially_resizer>

const order_type boost::numeric::odeint::velocity_verlet< Coor, Velocity, Value, Acceleration, Time, TimeSq, Algebra, Operations, Resizer >::order_value = 1

static

Referenced by boost::numeric::odeint::velocity_verlet< Coor, Velocity, Value, Acceleration, Time, TimeSq, Algebra, Operations, Resizer >::order().

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The documentation for this class was generated from the following file:

• boost_1_57_0/boost/numeric/odeint/stepper/velocity_verlet.hpp